Running head: z-Scores, Type I and Type II Error, Null Hypothesis Testing ANSWER TEMPLATE 1

z-Scores, Type I and Type II Error, Null Hypothesis Testing ANSWER TEMPLATE 2

## z-Scores, Type I and Type II Error, Null Hypothesis Testing Answer Template

## Student Name

## Capella University

# z-Scores, Type I and Type II Error, Null Hypothesis Testing Answer Template

The following assignment includes three sections consisting of:

1. *z *scores in SPSS.

2. Case studies of Type I and Type II errors.

3. Case studies of null hypothesis testing.

Additional notes:

· Answer in complete sentences.

· Follow APA rules for scholarly writing.

· Include a reference list if necessary.

· Save your answers and upload this template to the assignment area for grading.

## Section 1: *z* Scores in SPSS

A *z *score is typically analyzed when population mean (µ) and population standard deviation (σ) are known. However, in SPSS, we can still calculate *z *scores with the **grades.sav **data using the sample mean (*M*) and sample standard deviation (*s*). To do this, open **grades.sav **in SPSS. On the **Analyze** menu, point to **Descriptive Statistics**, and then click **Descriptives…**

You will be calculating and interpreting *z *scores for the **total **variable. In the **Descriptives** dialog box, move the **total **variable into the **Variable(s)** box. Select the **Save standardized values as variables **option and click **OK**.

SPSS provides descriptive statistics for **total** in the **Output** window. SPSS also creates a new variable in the far right column, labeled **Ztotal**, in the **Data Editor** area**. Ztotal** provides a *z *score for each case on the **total **variable. You are now prepared to answer the following Section 1 questions.

### Question 1

What is the sample mean (*M*) and sample standard deviation (*s*) for **total**? You will use these values in Question 2 below.

[Answer here in complete sentences. Also insert the output from SPSS here. Replace this prompt and the prompts below, using as much space as necessary to answer questions.]

### Question 2

A *z* score for this sample is calculated as [(*X* – *M*) ÷ *s*]. Locate Case #53’s unstandardized **total **score (*X*) in the **Data Editor**. In the formula below, replace *X*, *M*, *s*, and ? to show how the *z *score in **Ztotal **is derived for Case #53.

(*X *– *M* ) ÷ *s* = ?

### Question 3

Run **Descriptives…** on **Ztotal**. What are the mean and standard deviation of **Ztotal**? (Hint: “0E7” in SPSS is scientific notation for 0). Are the mean and standard deviation what you would expect? Justify your answer.

[Answer here in complete sentences. Also place the SPSS output here.]

### Question 4

Case number 6 has a **Ztotal **score of 1.19. What does a *z* value of 1.19 represent?

[Answer here in complete sentences.]

### Question 5

Identify the case with the lowest *z* score. Refer to Appendix A in the Warner (2013) text. Interpret the percentile rank of this *z* score rounded to whole numbers.

[Answer here in complete sentences.]

### Question 6

Identify the case with the highest *z* score. Refer to Appendix A in the Warner (2013) text. Interpret the percentile rank of this *z* score rounded to whole numbers.

[Answer here in complete sentences.]

## Section 2: Cases Studies of Type I and Type II Errors

### Question 7

A jury must determine the guilt of a criminal defendant (not guilty, guilty). Identify how the jury would make a correct decision. Analyze how the jury would commit a Type I error versus a Type II error.

[Answer here in complete sentences.]

### Question 8

An I/O psychologist asks employees to complete surveys measuring job satisfaction and organizational citizenship behavior. She intends to measure the strength of association between these two variables. The researcher is concerned that she will commit a Type I error. What research decision influences the magnitude of risk of a Type I error in her study?

[Answer here in complete sentences]

### Question 9

A clinical psychologist is studying the efficacy of a new drug medication for depression. The study includes a placebo group (no medication) versus a treatment group (new medication). He then measures the differences in depressive symptoms across the two groups.

What would a Type I error represent within the context of his study? How can he reduce the risk of committing a Type I error? How does this decision affect the risk of committing a Type II error?

[Answer here in complete sentences.]

## Section 3: Case Studies of Null Hypothesis Testing

### Question 10

You are running a series of statistical tests in SPSS using the standard criterion for rejecting a null hypothesis. You obtain the following *p* values.

Test 1 calculates group differences with a *p* value = .07.

Test 2 calculates the strength of association between two variables with a *p* value = .50.

Test 3 calculates group differences with a *p* value = .001.

For each test below, state whether or not you reject the null hypothesis. For each test, also explain what your decision implies in terms of group differences (Test 1 and Test 3) and in terms of the strength of association between two variables (Test 2).

Test 1 (group differences) =

Test 2 (strength of association) =

Test 3 (group differences) =

### Question 11

A researcher calculates a statistical test and obtains a *p* value of .86. He decides to reject the null hypothesis. Is this decision correct, or has he committed a Type I or Type II error? Explain your answer.

[Answer here in complete sentences]

### Question 12

You are proposing a research study that you would like to conduct while attending Capella University. During the proposal, a committee member asks you to explain in your own words what you meant by saying “*p* less than .05.” Provide an explanation.

[Answer here in complete sentences]

# References

Provide references if necessary. Save your answers and upload this template to the assignment area.

Warner, R. M. (2013). *Applied statistics: From bivariate through multivariate techniques* (2nd ed.). Thousand Oaks, CA: Sage.